The determination of underlying, unknown or hidden states of a system from noisy observations of the system is a fundamental classification problem relevant to various system diagnostics and data analytics applications.
A classification method that addresses this problem takes as input acquired data, and outputs estimates of the underlying states, or other relevant information regarding the states.
For example, a system may be in either a normal or broken state. In general, there can be many more than two relevant states, e.g., “failure in component X, Y or Z, etc.”, and the system can switch between these states over time. These states cannot be directly observed. Instead, only noisy data, that are somehow related to the underlying states, can be acquired. Determining whether the system is operating normally or is broken is a matter of inferring the underlying state from the acquired data.
A model for the noisy data and the unknown temporally-evolving state can be a hidden Markov model (HMM). Parameters of the HMM include statistical distributions describing how the state evolves over time, and how the data are related to the underlying states. Given knowledge of these parameters, the Viterbi classification method outputs a most likely sequence of the underlying states that produced the acquired data. Lacking knowledge of the model parameters can make the design of the classification method significantly more difficult.
In a simple method, a client acquires the noisy data and has a classification method. However, when the client is resource constrained, a server can assists the client in estimating the underlying hidden states. The motivation for such a two-party coordination between the client and the server can be due to asymmetries of information or capabilities of the client and server, e.g., the server may have exclusive information about a system model, better classification methods, and better computational resources. In a case of information asymmetry, it may be that neither the client nor the server alone have full knowledge of the system parameters, and thus the coordination of the two parties may serve to jointly produce a better reconstruction than either could do alone.
Naturally, there may be privacy concerns for both the client and the server in participating in this coordination. The client desires to protect the privacy of the acquired data and the estimated states. The server desires to protect the privacy of its exclusive knowledge of the system parameters and its classifier.